BSA Flow Software Installation and User's Guide - CSI

N−1
Mean u ∑ ηiui
=
i=
0
N−1
∑ i i
i=
0
2
Variance σ = η ( − )
2
(Output)
u u (Not Output)
2
RMS σ = σ
(Output)
N−1
1
3
i=
0
Skewness S= ∑ i( ui
− )
Flatness F= ∑ i( ui
− )
σ
N−1
1
4
i=
0
σ
3
η u (Output)
4
η u (Output)
N−1
∑ η
Cross-Moments uv − u v = i( u i − u)( v i − v)
i=
0
Table 5-4: Formulas for estimating moments.
The weighting factor ηi can be set to either
ηi =
N
1 (Arithmetic weighting)
or
η i
=
t
i
N−1
∑ t j
j=
0
(Transit time weighting).
(Output)
where N is the number of velocity samples, and ti is the transit time of the
i’th seeding particle passing the LDA measuring volume. (Transit Time is
sometimes referred to as residence time).
Arithmetic weighting should only be used if the velocity-samples are
independent, meaning that the time between samples exceeds twice the
integral timescale of the flow. This can be achieved using the controlled
dead time mode of acquisition. The user has to estimate the integral
timescale and set the dead-time interval accordingly. If this is violated,
mean-velocity will be biased towards higher velocities, and higher order
moments will be affected as well. In such cases transit time weighting should
be used instead: This takes a little longer to compute, but results are biasfree.
MeanConf and RMSConf: 95% confidence limits of the Mean and RMS
values. Read more in section 5.14.3.
Anode current: this is the mean photo-multiplier output current, which is a
measure of light intensity. It can help the user to determine the accurate
position of a solid surface in boundary layer experiments, or find the most
dense part of a spray.
Analog Monitor: available if the Analog Monitor option is installed. See
chapter 6 for details.
AD Mean and AD RMS: available if the Analog Input option is installed.
See chapter 6 for details.
BSA Flow Software: Project explorer objects 5-73